Properties

Label 2.2.321.1-3.1-b
Base field \(\Q(\sqrt{321}) \)
Weight $[2, 2]$
Level norm $3$
Level $[3, 3, -2w + 19]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\sqrt{321}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).

Form

Weight: $[2, 2]$
Level: $[3, 3, -2w + 19]$
Dimension: $2$
CM: no
Base change: no
Newspace dimension: $90$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} - 3x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}e$
2 $[2, 2, w + 1]$ $\phantom{-}e - 3$
3 $[3, 3, -2w + 19]$ $-1$
5 $[5, 5, w]$ $-2e + 3$
5 $[5, 5, w + 4]$ $-2e + 3$
13 $[13, 13, w + 1]$ $-1$
13 $[13, 13, w + 11]$ $-1$
17 $[17, 17, w + 3]$ $-2e + 3$
17 $[17, 17, w + 13]$ $-2e + 3$
19 $[19, 19, w + 6]$ $\phantom{-}6e - 9$
19 $[19, 19, w + 12]$ $-6e + 9$
37 $[37, 37, w + 2]$ $\phantom{-}3$
37 $[37, 37, w + 34]$ $\phantom{-}3$
49 $[49, 7, -7]$ $-2$
59 $[59, 59, -4w - 33]$ $\phantom{-}4e - 12$
59 $[59, 59, 4w - 37]$ $\phantom{-}4e$
61 $[61, 61, w + 28]$ $\phantom{-}11$
61 $[61, 61, w + 32]$ $\phantom{-}11$
71 $[71, 71, w + 22]$ $\phantom{-}3$
71 $[71, 71, w + 48]$ $-3$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -2w + 19]$ $1$